Van der Waals equation

The slope of tangent drawn on critical point is opposite on either side of this point.
The isothermal curve touching the critical point is critical isothermal.
The temperature, pressure and volume corresponding to critical point are known as critical temperature (T_c), critical pressure (P_c) and critical volume (V_c) respectively.
P_c, V_c and T_c are combindly known as critical constants.

Any gas can be liquified below its critical temperature.
Every gas has a critical temperature above which the gas can not be liquified by increasing pressure.
At critical temperature, the density of liquid and its saturated vapour are equal. Above this temperature we can not distinguish between the two states.
Near critical temperature, the compressibility of gas is very high and it become infinitive at critical temperature.
Above critical temperature, the gas behaves as permanent gas.
The liquid and gaseous state of substance are consistent and they are two distinct states of a long and continuous physical variation.

In derving the equation of ideal gas we assumed that
The gaseous molecules are infinitely smaller so that the volume occupied by them is negligible in comparison to the total volume of the gas, whereas the gaseous molecules have finite size.
The molecules does not attract each other, whereas they mutually attract each other.
So two corrections should be required for real gas equation, which are
Correction for finite size of molecule and
Correction for intermolecular attraction.
On the basis of it, the equation of state for real gas or Van der Waal equation of state is
(P+an₂/V₂)(V - nb) = RT.

The present lecture is a bilingual lecture, in which every step is explained in Hindi and in English language. Van der Waal equation of state is very important in Thermodynamics. In the present lecture the Van der Waal equation is explained in a well systematic way.